Problem: Simplify the following expression: $ q = \dfrac{-5x - 8}{8} - \dfrac{-7}{9} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-5x - 8}{8} \times \dfrac{9}{9} = \dfrac{-45x - 72}{72} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-7}{9} \times \dfrac{8}{8} = \dfrac{-56}{72} $ Therefore $ q = \dfrac{-45x - 72}{72} - \dfrac{-56}{72} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-45x - 72 + 56 }{72} $ Distribute the negative sign: $q = \dfrac{-45x - 72 + 56}{72}$ $q = \dfrac{-45x - 16}{72}$